Determination of young'S modulus of porous thin films using ultra-low load nano-indentation

Abstract

A method and computer product program for determining Young's modulus. The method includes placing a probe in contact with a surface of a material on a substrate and, with an initial force of 800 nano newtons or less; determining the location of the surface relative to an initial indentation depth for the initial force; increasing the force on the probe from the initial force to a maximum force greater than the initial force to generate a load curve; decreasing the force on the probe from the maximum force to the initial force to generate an unload curve, the maximum force selected such that the unload curve is independent of the presence of the substrate; and using the unload curve, determining a relationship between (i) the reduced modulus of the sample material and (ii) the ratio of probe penetration depth and the thickness of the layer.

What is claimed is: 
     
       1. A method, comprising:
 placing a probe, of a nano-indenter, in contact with a surface of a layer of a sample material on a substrate with an initial force of 800 nano newtons or less; 
 determining an area function of a tip of said probe on a layer of a standard material on said substrate; 
 measuring a low-k sample placed in said nano-indenter for measurement; 
 selecting an initial load, associated with said initial force, configured to balance requirements of a minimum surface perturbation with loads for stabilizing contact of the tip with respect to said low-k sample; 
 applying said initial load to said low-k sample; 
 measuring, based on said applying, a first displacement value; 
 selecting a maximum load associated with said initial load; 
 determining a location of said surface relative to an initial indentation depth for said initial force; 
 increasing the force on said probe from said initial force to a maximum force, associated with said maximum load, greater than said initial force to generate a load curve of force versus probe penetration depth; S/N: 14/607,291 2 
 decreasing the force on said probe from said maximum force to said initial force to generate an unload curve of force versus probe penetration depth, said maximum force selected such that the unload curve is independent of the presence of said substrate; and 
 using said unload curve, determining a relationship between (i) a reduced modulus of said sample material and (ii) a ratio of probe penetration depth and a thickness of said layer; 
 using said area function and said unload curve to extract said reduced modulus; and 
 using said reduced modulus, a Poisson's ratio of said sample material, a modulus of said standard material, and a Poisson's ratio of said standard material to determine a Young's modulus of said sample material. 
 
     
     
       2. The method of  claim 1 , wherein said relationship is described by a linear fit of a plot of (i) a log of said reduced modulus versus (ii) a log of said ratio of probe penetration depth to the thickness of said layer when a regression coefficient of said linear fit is greater or equal to 0.96. 
     
     
       3. The method of  claim 2 , wherein said relationship is described by a plot of (i) said reduced modulus versus (ii) said ratio of probe penetration depth to the thickness of said layer when said regression coefficient is less than 0.96. 
     
     
       4. The method of  claim 1 , including:
 after applying said initial force but before increasing the force on said probe from said initial force to said maximum force, lifting said probe away from said surface to locate the point of zero load and zero displacement. 
 
     
     
       5. The method of  claim 1 , including:
 between said increasing said force from said initial force to said maximum force and said decreasing said force from said maximum force to said initial force, holding said maximum force for a fixed period of time sufficient to allow for an increase in penetration depth at said maximum force before generating said unload curve. 
 
     
     
       6. The method of  claim 1 , wherein said layer of sample material comprises a porous material having a dielectric constant of less than 4. 
     
     
       7. The method of  claim 1 , wherein said maximum force is equal to less than 50 micro newtons. 
     
     
       8. The method of  claim 1 , wherein said maximum force is equal to less than 25 micro newtons. 
     
     
       9. The method of  claim 1 , wherein said maximum force is equal to less than 10 micro newtons. 
     
     
       10. The method of  claim 1 , wherein said probe penetrates into said layer between 0.1% and 60% of the thickness of said layer at said maximum force. 
     
     
       11. The method of  claim 1 , wherein said probe penetrates into said layer of said sample material greater than or equal to 10 nanometers. 
     
     
       12. The method of  claim 1 , wherein said probe has a tip comprising a cube corner and said cube corner has a radius of 40 nm or less. 
     
     
       13. The method of  claim 1 , wherein said layer of sample material is dry and said indentation is performed in a dry inert atmosphere. 
     
     
       14. A method, comprising:
 placing a probe, of a nano-indenter, in contact with a surface of a porous material on a substrate located in an inert atmosphere; 
 determining an area function of a tip of said probe on a layer of a standard material on said substrate; 
 measuring a porous material placed in said nano-indenter for measurement; 
 selecting an initial load, associated with an initial force, configured to balance requirements of a minimum surface perturbation with loads for stabilizing contact of the tip with respect to said porous material; 
 applying said initial load to said porous material; 
 measuring, based on said applying, a first displacement value; 
 selecting a maximum load associated with said initial load; 
 determining a location of the surface by applying a force of less than 800 nano newtons to the surface; 
 determining unload characteristics of the porous material using probe pressures selected such that (i) the unload characteristics of the porous material are unaffected by the presence of the substrate and (ii) the probe simultaneously induces elastic and plastic deformation of the porous material; and 
 performing data analysis of the unload characteristics to determine the relationship between (i) a modulus of the porous material and (ii) a ratio of contact depth to a thickness of the porous material; 
 using said area function and said unload characteristics to extract said modulus; and 
 using said modulus, a Poisson's ratio of said porous material, a modulus of said standard material, and a Poisson's ratio of said standard material to determine a Young's modulus of said porous material. 
 
     
     
       15. The method of  claim 14 , wherein the relationship is non-linear, and a log-log plot is employed to extract the modulus. 
     
     
       16. The method of  claim 15 , wherein the relationship is linear, and a linear-linear plot is employed to extract the modulus. 
     
     
       17. A computer program product for determining Young' modulus, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computer, to cause the computer to:
 instruct a nano-indentation device to place a probe, of a nano-indenter, in contact with a surface of a layer of a sample material on a substrate with an initial force of 800 nano newtons or less; 
 determine an area function of a tip of said probe on a layer of a standard material on said substrate; 
 measure a low-k sample placed in said nano-indenter for measurement; 
 select an initial load, associated with said initial force, configured to balance requirements of a minimum surface perturbation with loads for stabilizing contact of the tip with respect to said low-k sample; 
 apply said initial load to said low-k sample; 
 measure, based on applying said initial load to said low-k sample, a first displacement value; 
 select a maximum load associated with said initial load; 
 determine a location of said surface relative to an initial indentation depth for said initial force; 
 instruct said nano-indentation device to increase the force on said probe from said initial force to a maximum force, associated with said maximum load, greater than said initial force and to generate a load curve of force versus probe penetration depth; 
 instruct said nano-indentation device to decrease the force on said probe from said maximum force to said initial force and to generate an unload curve of force versus probe penetration depth, said maximum force selected such that the unload curve is independent of the presence of said substrate; 
 use said unload curve, determining a relationship between (i) a reduced modulus of said sample material and (ii) a ratio of probe penetration depth and a thickness of said layer; 
 use said area function and said unload curve to extract said reduced modulus; and 
 use said reduced modulus, a Poisson's ratio of said sample material, a modulus of said standard material, and a Poisson's ratio of said standard material to determine a Young's modulus of said sample material. 
 
     
     
       18. The computer program product of  claim 17 , wherein said relationship is described by a linear fit of a plot of (i) a log of said reduced modulus versus (ii) a log of said ratio of probe penetration depth to a thickness of said layer when a regression coefficient of said linear fit is greater or equal to 0.96. 
     
     
       19. The computer program product of  claim 18 , wherein said relationship is described by a plot of (i) said reduced modulus versus (ii) said ratio of probe penetration depth to the thickness of said layer when said regression coefficient is less than 0.96.